1 Answer

Flq · Answer 1 · 2023-07-22T20:26:14+0000

Answer:

-3. Option C is correct

Given the trigonometry equation shown below;

$sin\theta=(3√(10))/(10)=(opposite)/(hypotenuse)$

Find the adjacent side using the pythagoras theorem as shown:

$\begin{gathered} adj^2=hyp^2-opp^2 \\ adj^2=10^2-(3√(10))^2 \\ adj^2=100-90 \\ adj=√(10) \end{gathered}$

Determine the value of tan theta

$\begin{gathered} tan\theta=(opposite)/(adjacent) \\ tan\theta=(3√(10))/(√(10)) \\ tan\theta=3 \end{gathered}$

Since the angle theta is quadrant II and tan theta is negative in the second quadrant, hence;

$tan\theta=-3$